Problem: Write the equation of a line that is perpendicular to $y=-\dfrac{2}{7}x+9$ and that passes through the point $(4,-6)$.
Answer: Getting started Key idea: The slopes of perpendicular lines are negative reciprocals of each other. Step 1: Find the slope Slope of the given line: ${-\dfrac{2}{7}}$ So, the slope of the perpendicular line: $C{\dfrac{7}{2}}$ Step 2: Substitute the known point into linear equation The perpendicular line will have a slope of $C{\dfrac{7}{2}}$ and pass through the point ${(4,-6)}$. Let's start from the point-slope form of the equation of the perpendicular line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{(-6)} &= C{\dfrac{7}{2}}(x-{4})\\\\\\ y+6 &= C{\dfrac{7}{2}}x -14 \\\\\\ y &= C{\dfrac{7}{2}}x { -20} \end{aligned}$ Answer $y=C{\dfrac{7}{2}}x {-20}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$